### Place

130 120 100 150
1st S T T S
2nd T S S T

This preference schedule can actually be simplified further.
Notice that the column headed 130 and the one headed 150 are the same. So, we could combine these two columns into one column headed 280 (130+150).
Also, the column headed 120 and the one headed 100 are the same. So, we could combine these two columns into one column headed 220 (120+100).
With these simplifications, the preference schedule above can be written more compactly as:

### Place

280 220
1st S T
2nd T S

It is up to you whether to simplify a preference schedule or not. There are advantages (simplifies subsequent work) and disadvantages (sometimes the extra time required to simplify is not offset by the time saved subsequently).

If you had trouble, think of it this way. Paul is out, so mark through all the P's in the preference schedule that still has Paul in it.

### Place

130 120 100 150
1st P T T S
2nd S S P P
3rd T P S T

Now, each candidate below P in each of the columns moves up one position producing the preference schedule below.

### Place

130 120 100 150
1st PS T T S
2nd T S PS PT
3rd   P

Since the P's are marked out, they can be taken out of the preference schedule and since there are no longer any entries in the 3rd place row, it can be eliminated to produce the final preference schedule.

130 120 100 150
1st S T T S
2nd T S S T

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